Question

The height h (in inches) above the water of a pelican before a dive is modeled by h=-16t^2+70t+50, where t is time (in seconds)

Answer 1

ANSWER

a) 5 seconds.

b) 50 inches.

EXPLANATION

The height of the pelican is modeled by,

$h(t) = - 16t^{2} + 70t + 50$

The pelican enters the when

$h(t) = 0$

$- 16t^{2} + 70t + 50 = 0$

Divide through by negative 2,

$8 {t}^{2} - 35t - 25 = 0$

Factor to obtain

$(t - 5)(8t + 5) = 0$

This implies that,

$t = 5 \: or \: t = - \frac{5}{8}$

Time cannot be negative, therefore the water after 5 seconds.

B) The height of the pelican is modeled by

$h(t) = - 16t^{2} + 70t + 50$

When

$t = 0$

$h(0) = - 16(0)^{2} + 70(0) + 50$

$h(0) = 50$

The pelican was 50 inches above the water at time t=0.